# 5: Electrostatics

- Page ID
- 3929

*Electrostatics* is the theory of the electric field in conditions in which its behavior is independent of magnetic fields, including

- The electric field associated with fixed distributions of electric charge
*Capacitance*(the ability of a structure to store energy in an electric field)- The
*energy*associated with the electrostatic field *Steady current*induced in a conducting material in the presence of an electrostatic field (essentially, Ohm’s Law)

The term “static” refers to the fact that these aspects of electromagnetic theory can be developed by assuming sources are time-invariant; we might say that electrostatics is the study of the electric field at DC. However, many aspects of electrostatics are relevant to AC, radio frequency, and higher-frequency applications as well.

- 5.1: Coulomb’s Law
- Consider two charge-bearing particles in free space. Let the charges borne by these particles be q1 and q2 , and let R be the distance between them. If the particles bear charges of the same sign, then the particles repel; otherwise, they attract. This repulsion or attraction can be quantified as a force experienced by each particle. Physical observations reveal that the magnitude of the force is proportional to the product of charges, and inversely proportional to R2 . For particle 2 we f

- 5.3: Charge Distributions
- The charge of a single electron is very small and we rarely deal with electrons one at a time, so it is usually more convenient to describe charge as a quantity that is continuous over some region of space. In particular, it is convenient to describe charge as being distributed in one of three ways: along a curve, over a surface, or within a volume.

- 5.4: Electric Field Due to a Continuous Distribution of Charge
- It is common to have a continuous distribution of charge as opposed to a countable number of charged particles. In this section, we extend the discrete perspective of charge distributions into the concept of continuous distribution of charge so that we may address this more general class of problems.

- 5.5: Gauss’ Law - Integral Form
- Gauss’ Law is one of the four fundamental laws of classical electromagnetics, collectively known as Maxwell’s Equations. Gauss’ Law states that the flux of the electric field through a closed surface is equal to the enclosed charge.

- 5.10: Kirchoff’s Voltage Law for Electrostatics - Integral Form
- Kirchoff’s Voltage Law for Electrostatics states that the integral of the electric field over a closed path is zero.

- 5.11: Kirchoff’s Voltage Law for Electrostatics: Differential Form
- The integral form of Kirchoff’s Voltage Law for electrostatics states that an integral of the electric field along a closed path is equal to zero. In this section, we derive the differential form of this equation. In some applications, this differential equation, combined with boundary conditions imposed by structure and materials and can be used to solve for the electric field in arbitrarily complicated scenarios.

- 5.19: Charge and Electric Field for a Perfectly Conducting Region
- In this section, we consider the behavior of charge and the electric field in the vicinity of a perfect electrical conductor (PEC).

- 5.21: Dielectric Breakdown
- All practical dielectrics fail with sufficiently strong electric field, which is abrupt and is observed as a sudden, dramatic increase in conductivity, signaling that electrons are being successfully dislodged from their host molecules. The threshold value of the electric field intensity at which this occurs is known as the dielectric strength, and the sudden change in behavior observed in the presence of an electric field greater than this threshold value is known as dielectric breakdown.

- 5.22: Capacitance
- Capacitance is the ability of a structure to store energy in an electric field.